If:
You can't get MySQLi to work.
And:
The database credentials you are using were created on an older version of MySQL (not sure how old, but most likely prior to MySQL 5.)
Then:
Your database password may need to be updated to use the newer authentication scheme.
There are instructions on how to do that out there. Here is one example: http://code.openark.org/blog/mysql/upgrading-passwords-from-old_passwords-to-new-passwords
Or, if you're lazy like me, just create a new user and password and assign it to the database. Don't forget to apply the appropriate permissions to the new user. Then use that new user and password for ZenPhoto.
...jim